In order to solve the problem that pedestrian trajectory prediction research only focuses on interactive information of historical trajectories and ignores interactive information of endpoints， a pedestrian trajectory prediction model based on Graph Convolutional Network （GCN） and Endpoint Induction was proposed， named GCN-EI. Firstly， a classification method was employed on the training set to learn the weighted distribution of potential future endpoints for pedestrians. Subsequently， the possible endpoints were connected with their corresponding historical trajectories， and the interactive features of pedestrians were extracted over a longer time span by using the GCN with attention mechanism and endpoint conditions. Meanwhile， an individual feature module was used to extract the internal motion characteristics of pedestrians. Finally， the future trajectory of pedestrian was predicted by the temporal inference convolution. Test results on ETH and UCY datasets show that compared to STITD-GCN （Spatio-Temporal Interaction and Trajectory Distribution GCN） model， the proposed model has the Average Displacement Error （ADE） and Final Displacement Error （FDE） decreased by 4.5% and 5.0%， respectively； moreover， compared to PCCSNet （Prediction via modality Clustering， Classification and Synthesis Network） model using classification method， it has the FDE decreased by 9.5% .